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Consider randomly selecting a student at a large university. Let A be the event that the selected student has a Visa card, let B be the analogous event for MasterCard, and let C be the event that the selected student has an American Express card. Suppose that P(A) = 0.6, P(B) = 0.4, and P(A n B) = 0.3, suppose that P(C) = 0.2, P(An C) = 0.12, P(B n C) = 0.1, and P(An Bn C) = 0.07. (a) What is the probability that the selected student has at least one of the three types of cards? 0.75 (b) What is the probability that the selected student has both a Visa card and a MasterCard but not an American Express card? 0.23 (c) Calculate P(B | A) and P(A | B). P(BIA) 05 P(AIB) 075 x X Interpret P(BIA) and P(A | B). (Select all that apply.) OP(AIB) is the probability that a student does not have a MasterCard or a Visa card. OP(BIA) is the probability that a student does not have a MasterCard or a Visa card. P(BIA) is the probability that given that a student has a MasterCard, they also have a visa card. OP(AIB) is the probability that given that a student has a Visa card, they also have a MasterCard. OP(AIB) is the probability that given that a student has a MasterCard, they also have a visa card. P(BIA) is the probability that given that a student has a Visa card, they also have a MasterCard. (d) If we learn that the selected student has an American Express card, what is the probability that she or he also has both a Visa card and a MasterCard? 0.35 (e) Given that the selected student has an American Express card, what is the probability that she or he has at least one of the other two types of cards? 763 X

Consider randomly selecting a student at a large university. Let A be the event that the selected student has a Visa card, let B be the analogous event for MasterCard, and let C be the event that the selected student has an American Express card. Suppose that P(A) = 0.6, P(B) = 0.4, and P(A n B) = 0.3, suppose that P(C) = 0.2, P(An C) = 0.12, P(B n C) = 0.1, and P(An Bn C) = 0.07. (a) What is the probability that the selected student has at least one of the three types of cards? 0.75 (b) What is the probability that the selected student has both a Visa card and a MasterCard but not an American Express card? 0.23 (c) Calculate P(B | A) and P(A | B). P(BIA) 05 P(AIB) 075 x X Interpret P(BIA) and P(A | B). (Select all that apply.) OP(AIB) is the probability that a student does not have a MasterCard or a Visa card. OP(BIA) is the probability that a student does not have a MasterCard or a Visa card. P(BIA) is the probability that given that a student has a MasterCard, they also have a visa card. OP(AIB) is the probability that given that a student has a Visa card, they also have a MasterCard. OP(AIB) is the probability that given that a student has a MasterCard, they also have a visa card. P(BIA) is the probability that given that a student has a Visa card, they also have a MasterCard. (d) If we learn that the selected student has an American Express card, what is the probability that she or he also has both a Visa card and a MasterCard? 0.35 (e) Given that the selected student has an American Express card, what is the probability that she or he has at least one of the other two types of cards? 763 X

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Please answer (c) and (e)
Consider randomly selecting a student at a large university. Let A be the event that the selected student has a Visa card, let B be the analogous event for MasterCard, and let C be the event that the selected student has an American Express card. Suppose that P(A) = 0.6, P(B) = 0.4, and PLA n B) = 0.3, suppose that P(C) = 0.2, P(An C) =0.12, P(B n C) = 0.1, and P(A n Bn C) = 0.07. (a) What is the probability that the selected student has at least one of the three types of cards? 0.75 (b) What is the probability that the selected student has both a Visa card and a MasterCard but not an American Express card? 0.23 (c) Calculate P(B | A) and P(AIB). P(BIA) = .05 P(A | B) = 075 X X Interpret P(BIA) and P(A | B). (Sellect all that apply.) P(AB) is the probability that a student does not have a MasterCard or a Visa card. OP(BIA) is the probability that a student does not have a MasterCard or a Visa card. P(BIA) is the probability that given that a student has a MasterCard, they also have a visa card. P(AB) is the probability that given that a student has a Visa card, they also have a MasterCard. OP(AIB) is the probability that given that a student has a MasterCard, they also have a Visa card. P(BIA) is the probability that given that a student has a Visa card, they also have a MasterCard. X (d) If we learn that the selected student has an American Express card, what is the probability that she or he also has both a Visa card and a MasterCard? 0.35 (e) Given that the selected student has an American Express card, what is the probability that she or he has at least one of the other two types of cards? 763 x
Transcribed Image Text:Consider randomly selecting a student at a large university. Let A be the event that the selected student has a Visa card, let B be the analogous event for MasterCard, and let C be the event that the selected student has an American Express card. Suppose that P(A) = 0.6, P(B) = 0.4, and PLA n B) = 0.3, suppose that P(C) = 0.2, P(An C) =0.12, P(B n C) = 0.1, and P(A n Bn C) = 0.07. (a) What is the probability that the selected student has at least one of the three types of cards? 0.75 (b) What is the probability that the selected student has both a Visa card and a MasterCard but not an American Express card? 0.23 (c) Calculate P(B | A) and P(AIB). P(BIA) = .05 P(A | B) = 075 X X Interpret P(BIA) and P(A | B). (Sellect all that apply.) P(AB) is the probability that a student does not have a MasterCard or a Visa card. OP(BIA) is the probability that a student does not have a MasterCard or a Visa card. P(BIA) is the probability that given that a student has a MasterCard, they also have a visa card. P(AB) is the probability that given that a student has a Visa card, they also have a MasterCard. OP(AIB) is the probability that given that a student has a MasterCard, they also have a Visa card. P(BIA) is the probability that given that a student has a Visa card, they also have a MasterCard. X (d) If we learn that the selected student has an American Express card, what is the probability that she or he also has both a Visa card and a MasterCard? 0.35 (e) Given that the selected student has an American Express card, what is the probability that she or he has at least one of the other two types of cards? 763 x
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Consider randomly selecting a student at a large university. Let A be the event that the selected student has a Visa card, let B be the analogous event for MasterCard, and let C be the event that the selected student has an American Express card. Suppose that P(A) = 0.6, P(B) = 0.4, and P(A n B) = 0.3, suppose that P(C) = 0.2, P(An C) = 0.12, P(B n C) = 0.1, and P(A n Bn C) = 0.07. (a) What is the probability that the selected student has at least one of the three types of cards? 0.75 (b) What is the probability that the selected student has both a Visa card and a MasterCard but not an American Express card? 0.23 (c) Calculate P(B | A) and P(AIB). P(BIA) = .05 P(A | B) = 075 X X Interpret P(BIA) and P(A | B). (Sellect all that apply.) P(AIB) is the probability that a student does not have a MasterCard or a Visa card. OP(BIA) is the probability that a student does not have a MasterCard or a Visa card. P(BIA) is the probability that given that a student has a MasterCard, they also have a visa card. P(AIB) is the probability that given that a student has a Visa card, they also have a MasterCard. OP(AIB) is the probability that given that a student has a MasterCard, they also have a Visa card. P(BIA) is the probability that given that a student has a Visa card, they also have a MasterCard. X (d) If we learn that the selected student has an American Express card, what is the probability that she or he also has both a Visa card and a MasterCard? 0.35 (e) Given that the selected student has an American Express card, what is the probability that she or he has at least one of the other two types of cards? 763 x
Transcribed Image Text:Consider randomly selecting a student at a large university. Let A be the event that the selected student has a Visa card, let B be the analogous event for MasterCard, and let C be the event that the selected student has an American Express card. Suppose that P(A) = 0.6, P(B) = 0.4, and P(A n B) = 0.3, suppose that P(C) = 0.2, P(An C) = 0.12, P(B n C) = 0.1, and P(A n Bn C) = 0.07. (a) What is the probability that the selected student has at least one of the three types of cards? 0.75 (b) What is the probability that the selected student has both a Visa card and a MasterCard but not an American Express card? 0.23 (c) Calculate P(B | A) and P(AIB). P(BIA) = .05 P(A | B) = 075 X X Interpret P(BIA) and P(A | B). (Sellect all that apply.) P(AIB) is the probability that a student does not have a MasterCard or a Visa card. OP(BIA) is the probability that a student does not have a MasterCard or a Visa card. P(BIA) is the probability that given that a student has a MasterCard, they also have a visa card. P(AIB) is the probability that given that a student has a Visa card, they also have a MasterCard. OP(AIB) is the probability that given that a student has a MasterCard, they also have a Visa card. P(BIA) is the probability that given that a student has a Visa card, they also have a MasterCard. X (d) If we learn that the selected student has an American Express card, what is the probability that she or he also has both a Visa card and a MasterCard? 0.35 (e) Given that the selected student has an American Express card, what is the probability that she or he has at least one of the other two types of cards? 763 x
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